This interactive simulation models the motion of a simple pendulum. Users can change length, initial angle, and mass. Adjust the acceleration due to gravity to simulate pendulum motion on another planet. Graphs of angular position, angular velocity, and angular acceleration may be displayed, as well as energy bar graphs and free-body diagrams.

This applet was created with EJS, Easy Java Simulations, a modeling tool that allows users without formal programming experience to generate computer models and simulations.

9-12: 4E/H1. Although the various forms of energy appear very different, each can be measured in a way that makes it possible to keep track of how much of one form is converted into another. Whenever the amount of energy in one place diminishes, the amount in other places or forms increases by the same amount.

9-12: 4E/H9. Many forms of energy can be considered to be either kinetic energy, which is the energy of motion, or potential energy, which depends on the separation between mutually attracting or repelling objects.

4F. Motion

6-8: 4F/M3a. An unbalanced force acting on an object changes its speed or direction of motion, or both.

9-12: 4F/H8. Any object maintains a constant speed and direction of motion unless an unbalanced outside force acts on it.

11. Common Themes

11B. Models

3-5: 11B/E3. A model of something is similar to, but not exactly like, the thing being modeled. Some models are physically similar to what they are representing, but others are not.

6-8: 11B/M2. Mathematical models can be displayed on a computer and then modified to see what happens.

Common Core State Standards for Mathematics Alignments

Standards for Mathematical Practice (K-12)

MP.4 Model with mathematics.

Functions (8)

Use functions to model relationships between quantities. (8)

8.F.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

High School — Algebra (9-12)

Creating Equations^{?} (9-12)

A-CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

High School — Functions (9-12)

Interpreting Functions (9-12)

F-IF.7.e Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

Trigonometric Functions (9-12)

F-TF.1 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.

F-TF.4 (+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.

F-TF.5 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.^{?}

<a href="http://www.compadre.org/portal/items/detail.cfm?ID=9409">Duffy, Andrew. Boston University Physics Easy Java Simulation: Simple Pendulum. August 27, 2009.</a>

Duffy, A. (2009, August 27). Boston University Physics Easy Java Simulation: Simple Pendulum. Retrieved April 1, 2015, from http://physics.bu.edu/~duffy/Ejs/EP_chapter12/pendulum_v2d.html

Duffy, Andrew. Boston University Physics Easy Java Simulation: Simple Pendulum. August 27, 2009. http://physics.bu.edu/~duffy/Ejs/EP_chapter12/pendulum_v2d.html (accessed 1 April 2015).

%A Andrew Duffy %T Boston University Physics Easy Java Simulation: Simple Pendulum %D August 27, 2009 %U http://physics.bu.edu/~duffy/Ejs/EP_chapter12/pendulum_v2d.html %O application/java

%0 Electronic Source %A Duffy, Andrew %D August 27, 2009 %T Boston University Physics Easy Java Simulation: Simple Pendulum %V 2015 %N 1 April 2015 %8 August 27, 2009 %9 application/java %U http://physics.bu.edu/~duffy/Ejs/EP_chapter12/pendulum_v2d.html

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A standards-based module on the pendulum for grades 7-9 that includes lesson plan, student activity sheets, assessment, related simulations, and background information.

A link to the Easy Java Simulations Modeling and Authoring tool, needed to explore the computational model used in the simple pendulum model (cost free)

This is the full index of Easy Java Simulations (EJS) by author Andrew Duffy, created for first-semester introductory physics. EJS is a modeling tool developed by the Open Source Physics project.